空间柔性网—膜结构分析的数学规划算法

Mathematical Programming Method for Numerical Analysis of Flexible Net-Membrane Structures

提出了以参数变分原理为基础的数学规划算法 ,以计算分析太空用品中网 -膜结构起皱现象。针对网状柔性结构分析 ,算法的原理是将结构化成多个具有一定非线性本构关系的杆单元 ,并在此基础上进行杆系结构非线性分析的规划算法构造 ,可以较好地模拟网状柔性结构的起皱性质。而对于一般的膜结构 ,则构造了用于直接分析的膜单元相对应的本构模型 ,并在此基础上构造问题的求解算法。不同于常规的数值计算方法 ,提出的算法不依赖于应力的迭代过程。参数变分原理和数学规划算法的应用 ,使本算法可以很有效地分析预测网 -膜起皱的区域、模式和应力分布 ,从而为解决网 -膜结构起皱问题提供依据。

This paper gives a detailed introduction to the development of a new method for numerical simulation of the wrinkled behavior of space flexible structures. The flexible net-structure is modeled as a network of bars with a special nonlinear constitutive relationship. Based on the parametric variational principle, a mathematical programming method is developed for the nonlinear analysis of the network of bars. For the analysis of the membrane structure, a new method is developed to simulate directly the mechanic behaviors of the structure. The method is based on the finite element method with membrane elements and is constructed in terms of the corresponding constitutive relationship, from which the nonlinear behavior of the structure can be truly simulated. Compared with the conventional methods, the new method can provide a good convergence property and hence can obtain accurate predictions of wrinkled regions/patterns and stress distributions of the membrane structures. Numerical examples are presented to illustrate the validity and efficiency of the method proposed.